You decide to contribute to a mutual fund that averages 45 r

You decide to contribute to a mutual fund that averages 4.5% return per year. If you contribute $550 quarterly.
Round all answers to the nearest cent as needed.
a) How much will be in the account after 20 years? $

b) How much of this money did you deposit? $

c) How much of this money is interest earned? $

Solution

a) The formula for the future value ( F) of an annuity/recurring deposit is F = p [ ( 1 +r)ⁿ -1] / r where P is the periodic payment, r is the interest rate in decimals, per term and n is the number of periods. Here P = $ 550, r = (4.5/100)* ¼ = 0.01125 and n = 20*4 = 80. Therefore, F = 550[ (1 + 0.01125)⁸⁰ -1] /(0.01125) = 550 [( 1.01125)⁸⁰ -1]/( 0.01125) = 550(2.447274977 – 1)/( 0.01125) = 550*(1.447274977)/(0.01125) = 796/(0.01125) = $70755.67

b) The money deposited is $ 550 *20*4 = $ 44000.

c) The interest earned = Maturity value of the annuity – money deposited = $ 70755.67 - $ 44000 = $ 26755.67